# Algebra

Learn about functions, graphs, lines, and polynomials. "Algebra" is the math for describing how different things are related.

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Locating integers and non-integers on the number line
Using the number line to add numbers
Moving left on the number line
What happens when you add negative numbers?
The "size" of a number, or how far it is from zero
Ways to find the distance between any two numbers
2. Multiplication and division
Multiplying positive numbers, in any order
Discover what happens when you multiply by 1 and 0
Dividing positive numbers, and ways to think about it
An operation you just can't perform...
Is there more than one way to evaluate an expression?
Getting rid of parentheses when you add and multiply
What happens when you multiply negatives together?
What happens when you divide negative numbers?
Distributing a negative flips the signs
What to do when you have too many parentheses!
Discover how to find the "average" of numbers
3. Factoring
Dividing by a factor always gives you a whole number
Their only factors are 1 and themselves
Pulling out common factors using the distributive law
Flip the signs when you factor out negative numbers
The biggest factor that numbers have in common
When two numbers have no common factors
A 2000-year-old way to calculate the GCF
What you get when you multiply numbers by integers
The smallest multiple numbers have in common
4. Fractions
Draw and compare fractions, and convert to decimals
What's 1/2 times 3/5? Learn the trick in this lesson!
How to tell when fractions are equal or which is bigger
Simplifying fractions by removing common factors
Add and subtract fractions using common denominators
Dividing by a fraction is really multiplying by its reciprocal!
A number's multiplicative inverse is 1 over the number
Switching between mixed and improper fractions
The distributive law works for multiplying, but also dividing
Evaluating fractions of numbers (like 5/7 of 210)
5. Powers and roots
Multiplying a number by itself
Squaring, cubing, raising to the fourth, and so on...
Work backwards to find the number that was squared
How to find the roots of numbers that are NOT square
Do negative numbers even have square roots?
Cube roots, fourth roots, fifth roots, and so on...
Order of operations, now with exponents!
6. Rules for powers
A rule for multiplying one power by another
A rule for dividing one power by another
A rule for raising one power to another
It works for multiplication and division, but that's it!
What happens when you raise a number to the zero?
What does it mean to raise to a NEGATIVE exponent?
Taking a root is really the same as raising to a power
What does it mean to raise to the 2/3 power?
Roots are also exponents, so the same rules apply!
Getting smaller numbers under the root
7. Solving equations
Solve for unknown values using the number line
Learn how to evaluate expressions with variables
Adding or subtracting on both sides of equations
Multiplying or dividing on both sides of equations
A quick way to solve equations with fractions
Numbers in front of variables
Sometimes it takes more than one step to solve!
Solving equations when they have more than one variable
Some equations have no solutions, others have plenty!
8. Inequalities and simultaneous equations
Plotting inequalities on the number line
Solving and plotting multi-step inequalities
What happens when you multiply by a negative
Solve for both variables when you have two equations
Sometimes two equations have no solutions, or many!
9. Coordinates
Plotting points and finding their coordinates
The four quadrants, and the coordinates they contain
Given two points, which point is exactly halfway between?
10. Slope
A number that tells you the steepness of a line
How to calculate the slope between any two points
Discover what it means when slope is negative
What are the slopes of horizontal and vertical lines?
Two steps that will always give you the correct slope
Explore why parallel lines have the same slope
Discover how slopes of perpendicular lines relate
11. Lines
Turn an equation into your very first graph!
Turning an equation into a line, and vice versa
A formula for when you know the slope and coordinates
Forget equations, let's just look at the graphs!
Figuring out where lines cross the x- and y-axes
Given two lines, can you determine where they cross?
Exploring a graph that's not a line
Simplify inequalities with two variables and test solutions
Graph inequalities on the coordinate plane
12. Polynomials
Learn about a common type of algebraic expression
Computing sums and differences of polynomials
Multiply and divide polynomials with one term
Multiply binomials together using FOIL
How to multiply polynomials with many terms
A neat trick for simplifying certain binomials